“Writing across the curriculum,” “inquiry-based learning,” “collaborative learning,” “capstone experiences” — all are common phrases heard in academia. Looking specifically at mathematics, the phrases “calculus reform” and “quantitative literacy” come readily to mind. The widespread use of these phrases reflects successful reform movements designed to improve the educational experiences of college students. In Innovative Approaches, a series of papers are presented that show how similar reform principles are being applied in post-calculus mathematics courses. The papers resulted from a session at the 2001 Mathfest in which participants discussed the question, “What can be done to generate and then maintain student interest in the mathematics courses that follow calculus?”

The papers present innovative approaches to teaching mathematics in general, to teaching a specific course, or to teaching a specific topic in a course. Sufficient background information, sample assignments, examples of students’ work and grading/assessment strategies are included in most of the papers. The authors of some of the papers discuss difficulties they have encountered in implementing the innovations and make suggestions for others who are considering similar innovations at their own schools. It should be noted that the authors of the papers come from a wide variety of schools (public and private, research and teaching), which suggests that such innovations can be accomplished at any school with any student population.

I was not surprised to find that every one of the papers presented could be classified using one of the reform phrases above; they are, after all, well established reform movements. Many of the innovations involved the familiar format of an individual or team project followed by a presentation. What made the projects interesting was the degree of difficulty of the projects, the amount of mathematics the students were going to have to learn on their own in order to complete the project, the open-ended nature of some of the investigations undertaken by the students, and the possibility of continuing the project beyond the scope of the course into a senior or capstone project. It was also nice to find innovations for courses such as abstract algebra, topology and real analysis. The reader will also find the cited references useful for obtaining more information about the innovations.

There is a tendency when reading a book of this nature to be overwhelmed, thinking that it would be impossible to make similar changes in one’s own classes. In fact, several of the authors describe the pitfalls they encountered and report spending considerably more time on their classes after implementing the innovations. In spite of these negatives, however, the authors overwhelmingly report an increase in their own satisfaction with the course and an increase in student interest in the subject matter. Consequently, I recommend this book both enthusiastically and cautiously, and advise the reader to take the advice given by several of the authors: begin with small changes and expand after gaining confidence in a new teaching style.